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Binary search tree
A binary search tree is a binary tree where in each node: * The left subtree contains only nodes with keys less than the node's key (the "data"/"value" of the node). * The right subtree contains only nodes with keys greater than the node's key. * Both subtrees are also binary search trees. It follows that each key is distinct. Binary search trees are especially useful in constructing other data structures such as sets, multisets and associative arrays. Operations Searching Searching a binary search tree can easily be done using either an iterative or recursive method. Starting with the root node, we check to see if the current node contains the key we are searching for. If yes, then the key is found. If not, we do the search on the left subtree if the key is less, or the right subtree if the key is greater. We end the search when there is no existing child corresponding to the key (hence no subtree). ; Recursive This is a recursive algorithm for returning the value of a generic associative array implementation of a binary search tree, where valuetype is the type of the values. The type of the key is a comparable type where the operators <, > and = are defined. search(key) as valuetype return search(root, key) search(node, key) as valuetype if node is null then return null if key < node.key then return search(code.leftchild, key) else if key > node.key then return search(node.rightchild, key) else // equal return false.value ; Iterative search_iterative(key) as valuetype return search_iterative(root, key) search_iterative(node, key) as valuetype currentnode = node while node is not null if key < node.key then node = node.leftchild else if key > node.key then node = node.rightchild else // equal return node.value return false // exited while loop, null child Insertion As with searching, we find a location where we would insert the new node. This is done recursively until we find a free node where we could insert the new node. ; Recursive insert(key, value) insert(root, key, value) insert(ref node, key, value) if node is null node = new node with key = key, value = value else if key < node.key insert(node.leftchild, key, value) else if key > node.key insert(node.rightchild, key, value) else throw new exception with message = "key already exists in tree" ; Recursive, without references insert(node, key, value) if key < node.key if node.leftchild is null then node.leftchild = new node with key = key, value = value else insert(node.leftchild, key, value) else if key > node.key if node.rightchild is null then node.rightchild = new node with key = key, value = value else throw new exception with message = "key already exists in tree" Traversal We can use an inorder traversal to traverse through the nodes in the tree in order (of the keys). ; Algorithm (recursive) traverse() as list of node return traverse(root) traverse(node) as list of node list = new list of node list.add(traverse(node.leftchild)) list.add(node) list.add(traverse(node.rightchild)) return list Sorting A binary search tree can be used to implement a simple sorting algorithm. ; Algorithm sort(list of t) as list of t tree = new binarysearchtree(t, t) for each item in list tree.insert(item, null) return keys in tree.traverse Category:Data structures